Question

Drag the tiles to the boxes to form correct pairs.Consider functions fand g.(1) = 1 - 12g(x) = VII – 45Evaluate each combined function, and match it to the corresponding value.0VISV3 - 3-303(9.5) (2)(+) (2)(9 - 1)(-1)(-1)

Answer 1

We have the following functions:

$\begin{gathered} f(x)=1-x^2, \\ g(x)=\sqrt[]{11-4x}\text{.} \end{gathered}$

1) We evaluate (g · f)(2):

$(g\cdot f)(2)=g(2)\cdot f(2)=\sqrt[]{11-4\cdot2})\cdot(1-2^2)=-3\cdot\sqrt[]{3}\text{.}$

2) We evaluate (g + f)(2):

$(g+f)(2)=g(2)+f(2)=(\sqrt[]{11-4\cdot2})+(1-2^2)=\sqrt[]{3}-3.$

3) We evaluate (g - f)(-1):

$(g-f)(-1)=g(-1)-f(-1)=\sqrt[]{11-4\cdot(-1)}-(1-(-1)^2)=\sqrt[]{15}\text{.}$

4) We evaluate (f / g)(-1):

$(\frac{f}{g})(-1)=\frac{f(-1)}{g(-1)}=\frac{(1-(-1)^2)}{\sqrt[]{11-4\cdot(-1)}}=\frac{0}{4}=0.$

Answers

$\begin{gathered} (g\cdot f)(2)=-3\cdot\sqrt[]{3} \\ (g+f)(2)=\sqrt[]{3}-3 \\ (g-f)(-1)=\sqrt[]{15} \\ (\frac{f}{g})(-1)=0 \end{gathered}$