Question

Let f(x)=2x+3 and g(x)=x×x-1
find a. f(g(x)) b.g(f(x))

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Answer 1

See explanations below

Explanation:

Given the functions f(x)=2x+3 and g(x)=x^2-1

a. Find f(g(x))

f(g(x)) = f(x^2-1)

f(g(x)) = 2(x^2-1)+3

f(g(x))= 2x^2-2+3

f(g(x)) = 2x^2+1

Hence the composite function f(g(x)) is 2x^2+1

b) g(f(x)) = g(2x+3)

g(f(x) = (2x+3)^2-1

g(f(x)) = 4x^2+12x+9-1

g(f(x)) = 4x^2+12x+8