let (f(x)=5x^{2}-8) and (g(x)=3x). evaluate the following expressions and enter dne if the expression is…

Explanation:

Step1: Find $g(-1)$

Given $g(x)=3x$, substitute $x = - 1$. So $g(-1)=3\times(-1)=-3$.

Step2: Find $f(g(-1))$

Since $g(-1)=-3$ and $f(x)=5x^{2}-8$, substitute $x=-3$ into $f(x)$. Then $f(g(-1))=f(-3)=5\times(-3)^{2}-8=5\times9 - 8=45-8 = 37$.

Step3: Find $f(-1)$

Given $f(x)=5x^{2}-8$, substitute $x = - 1$. So $f(-1)=5\times(-1)^{2}-8=5 - 8=-3$.

Step4: Find $g(f(-1))$

Since $f(-1)=-3$ and $g(x)=3x$, substitute $x=-3$ into $g(x)$. Then $g(f(-1))=g(-3)=3\times(-3)=-9$.

Answer:

a) 37 b) -9