Question

given that $f(x)=3x + 7$ and $g(x)=2 - x^{2}$, calculate (a) $f(g(0))=$ (b) $g(f(0))=$ question help: video 1 video 2

Explanation:

Step1: Calculate $g(0)$

Substitute $x = 0$ into $g(x)=2 - x^{2}$. So $g(0)=2-0^{2}=2$.

Step2: Calculate $f(g(0))$

Since $g(0) = 2$, substitute $x = 2$ into $f(x)=3x + 7$. Then $f(g(0))=f(2)=3\times2 + 7=6 + 7=13$.

Step3: Calculate $f(0)$

Substitute $x = 0$ into $f(x)=3x + 7$. So $f(0)=3\times0+7 = 7$.

Step4: Calculate $g(f(0))$

Since $f(0)=7$, substitute $x = 7$ into $g(x)=2 - x^{2}$. Then $g(f(0))=g(7)=2-7^{2}=2 - 49=-47$.

Answer:

(a) 13
(b) -47