Consider the following equations: f(x)=5x^{2}+4 and g(x)=

alka8q7

alka8q7

Answered question

2021-11-30

Consider the following equations:
f(x)=5x2+4 and g(x)=2x
xf(x)G(x)012345678910
a) As x increases, will the value of f(x) always be greater than the value of g(x)?
b) Will an exponential function eventually always succeed a qudratic function?

Answer & Explanation

Royce Moore

Royce Moore

Beginner2021-12-01Added 17 answers

Step 1
We have f(x)=5x2+4, g(x)=2x
xf(x)g(x)04119222422=434923=845×42+4=8424=1655×52+4=12925=3265×62+4=18426=6475×72+4=24927=12885×82+4=32428=25695×92+4=40929=512105×102+4=504210=1024
Step 2
a) No, colen x=9, and x=10 the value of f(x) is oless than value of g(x), other interval [9, 10]
f(x)=5x2+4, g(x)=2x
when x=9
f(9)=5×92+4=409
and g(9)=22=512
f(9)<g(9)
Step 3
Other the interval [0, 10], the exponentional function enequally succed the quadratic function from x=9 onwards
The value or g(x)=2x begin to exceed the values of f(x)=5x2+4 with in interval [9, 10]

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