Question

When f(x) = 3x – 5 and g(x) = 2x^2-5. Find f(g(x)).Choices: A. 2x + 3B. 2x – 3C. 4x + 1D. 3x + 2

Answer 1

Since the function f is defined with the rule:

`f(x)=3x-5`

To find f(g(x)), replace x by g(x):

`f(g(x))=3\cdot g(x)-5`

Since g(x)=2x^2-5, substitute g(x) for its expression:

`\begin{gathered} 3\cdot g(x)-5=3\cdot(2x^2-5)-5 \\ =3\cdot2x^2-3\cdot5-5 \\ =6x^2-15-5 \\ =6x^2-20 \end{gathered}`

Therefore:

`f(g(x))=6x^2-20`