Function Math Problems - Practice with Solutions

Find all functions $f : R \to R$ such that $x^{2} \cdot f (x) + f (1 - x) = 2 x - x^{4}$ $\forall x \in R$
My solution:
Replace x by $(1 - x)$ and by eliminating $f (1 - x)$
I obtained $f (x) = 1 - x^{2}$

pezgirl79u 2022-10-31

Given $f (x y) = f (x + y)$ and $f (11) = 11$ , what is $f (49)$ ?

gasavasiv 2022-10-30

If $x, y, α > 0$ and $x > y$ , then $x^{α} > y^{α}$
I know it's obvious when we use differnetation rule for exponential function, but I'm not allowed to. Is there any way I can show it clearly?

Jairo Decker 2022-10-30

Let $a, b \in R$ with a<b and $f : [a, b] \to [a, b]$ be a continuous function. If $a_{0}, a_{1}, . . ., a_{n} \in R$ and $a_{0} + a_{1} + a_{2} + . . . + a_{n} \neq 0$ and $a_{0} x + a_{1} f (x) + a_{2} f^{2} (x) + . . . + a_{n} f^{n} (x) = 0, \forall x \in [a, b]$ , prove that $a \cdot b < 0$

Rene Nicholson 2022-10-30

Prove: $\frac{f (x + g (x)) - f (g (x))}{x} \to f^{'} (0)$ as x approaches 0

klastiesym 2022-10-29

Can we say $f (x) = \frac{x}{\ln (x^{2})}$ has a removable discontinuity at $x = 0$ ?

Danika Mckay 2022-10-29

$f : R \to R$ be function satisfying $f (x + y) = f (x) . f (y)$ for all $x, y \in R$ and $l i m_{x \to 0} f (x) = 1$ then show that $f (r x) = (f (x))^{r}$ for all $r \in Q$

hogwartsxhoe5t 2022-10-29

Find a point of discontinuity, if any
$f (x) = \frac{2 x^{2} + 2 x - 60}{x^{2} - x - 20}$

blackdivcp 2022-10-29

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.
$f (x) = 9 x e^{x}$
Increasing:
a) $(- \infty, - 1)$
b) $(- 1, \infty)$
c) $(- \infty, 0)$
d) $(- \infty, \infty)$
e) $(0, \infty)$
f) no interval

Madilyn Quinn 2022-10-28

Use the binomial series to expand the function as a power series.
\frac{9}{(6+x)^3}

Winston Todd 2022-10-27

Assume p is an even function and q is an odd function, given p,q lies on the entire real line, determine if $p \circ q$ is an even or odd function
Fundamentally,
Even function: $f (x) = f (- x)$
Odd function: $f (x) = - f (x)$
can I say that $p \circ q$ is an odd function because:
$(p \circ q) (x) = p (q (- x)) = p (- q (x)) = - (p \circ q) (x)$ ?

ndevunidt 2022-10-26

If two periodic functions so that $X = X (t)$ and $Y = X (t + α)$ , with α unknown is there a way to extract $α$ from $X - Y$ ?

podvelkaj8 2022-10-26

Given that $f (x) = 4 x - x^{2}$ for $x \leq 2$ is invertible, find $f^{- 1} (x)$

ormaybesaladqh 2022-10-25

Need to solve the following product:
$\prod_{k = 1}^{N} 1_{{y_{k} \geq 1}}$
Is there a way to simplify it or write it in a closed-form expression?

Chaim Ferguson 2022-10-25

Can anyone invert
$y = a \cos (x) + b \sin (2 x)$
to give $x = f (y)$ ?

Jairo Decker 2022-10-25

Finding the range of $\frac{5 \cos x - 2 \sin^{2} x + 4 \sin x - 3}{6 | \cos x | + 1}$

Marley Meyers 2022-10-24

Let $f (x) = \frac{x + 4}{x + 6}$
Find $f^{- 1} (- 5) = ?$

cousinhaui 2022-10-24

Since every function can be divided in a even and a odd part:
$f_{e} (x) = \frac{f (x) + f (- x)}{2}$
$f_{o} (x) = \frac{f (x) - f (- x)}{2}$
$f (x) = f_{e} (x) + f_{o} (x)$
How can I obtain the function by it's even part?

robbbiehu 2022-10-22

Find the $lim_{n \to \infty} \frac{\sqrt{n^{2} + 1} + \sqrt{n}}{(n^{4} + 1)^{1 / 4} - \sqrt{n}}$

limfne2c 2022-10-22

Given $a \in R$ , such that the two roots in
$f (x) = x^{2} + a x + (2 a + 319)$
are both positive integers. Find a.

Dealing with function Math questions is never easy as these can be implemented virtually anywhere where Algebra is used. It means that starting with at least one function Math example from what has been provided below will help you. Of course, certain function Math problems will require more analysis and verbal explanations, yet these are also encountered as you look through the questions. Learn about the use of equations first! The functions Math problems are always based on the analytical part because the function Math equation always has only one answer for every unknown variable.

Algebra I

Functions in Algebra Examples