Compose the following function and state the domain of the composed function. f(x)= 1/x-1 g(x)= sqrt(1-x^2) a) g(f(-2))

Yulia

Yulia

Answered question

2021-01-10

Compose the following function and state the domain of the composed function.
f(x)=1x1
g(x)=1x2
a) g(f(2))

Answer & Explanation

Alannej

Alannej

Skilled2021-01-11Added 104 answers

To find g(f(−2)), substitute -2 for x in the function f(x)=1x1 and then 13 for x in the function g(x)=1x2, and simplify.
g(f(2))=g(121)
=1(13)2
=119
=919
=83
=223
Therefore, g(f(2))=223
To obtain the composite function (gf)(x), substitute f(x)=1x1 and g(x)=1x2 in the definition of composite function (gf)(x)=g[f(x)], and simplify.
(gf)(x)=g[f(x)]
=g|1x1|
=1(1x1)2
=(x1)21(x1)2
=(x22x+11x1
=x(x2)x1
Therefore, g[f(x)]=x(x2)x1
To determine the domain of the composite function (gf)(x), use the definition of the composite function g[f(x)]=x(x2)x1 and identify the values of x, for which the denominator is not equal to zero and radicand is positive.
x0
x20
x2
x10
x1
Hence, the domain of the composite function g[f(x)]=x(x2)x1 is

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