Question

If f(x)=3x-2 and g(x)=x^2+1, find f(g(-1)) and g(f(3))

Answer 1

Answer:

$f(g(-1))=4$

$g(f(3))=50$

Step-by-step explanation:

We know the definition of both functions: $f(x)=3x-2$, and $g(x)=x^2+1$

A) In order to evaluate what $f(g(-1)) is$, let's first investigate what g(-1) is using the definition for this function:

$g(x)=x^2+1\\g(-1)=(-1)^2+1\\g(-1)=1+1\\g(-1)=2$

Now let's find what f(2) is using f(x) definition: $f(x)=3x-2\\f(2)=3(2)-2\\f(2)=6-2\\f(2)=4$

B) In order to evaluate what $g(f(3)) is$, let's first investigate what f(3) is using the definition for this function:

$f(x)=3x-2\\f(3)=3(3)-2\\f(3)=9-2\\f(3)=7$

Now let's find what g(7) is using the definition for this function:

$g(x)=x^2+1\\g(7)=(7)^2+1\\g(7)=49+1\\g(7)=50$