Question

QF Q6.) Find the following function for a.

Answer 1

`(f * g)(x) =\ \textgreater \ f(g(x))`


`f(5x^2 - 3) = 2(5x^2 - 3) - 2`


`f(5x^2 - 3)= 10x^2-6-2`


`f(5x^2 - 3)= 10x^2+(-6-2)`


`f(5x^2 - 3)=10x^2-8`

Answer 2

Hello!

The given equation can be rewritten to read as follows:

(f · g)(x) = f(g(x))

In other words, insert the given value of g(x) in place of the variable found in f(x) as follows:

f(5x² – 3) = 2(5x² – 3) – 2

Now simplify the right side of the equation:

f(5x² – 3) = 10x² – 6 – 2

Combine like terms:

f(5x² – 3) = 10x² – 8

We have now proven that (f · g)(x) is equal to 10x² – 8.

I hope this helps!