Question

Answer the questions please asap.

Answer 1

16) -55

17) 15

18) -23

19) -22

Explanation:

Given functions:

`\begin{cases}f(x)=-x^2+8x-11\\g(x)=14-(2)/(3)x\\h(x)=-x-7\end{cases}`

Question 16

To find f(-4) - f(1), substitute x = -4 into function f(x), and x = 1 into function f(x), then subtract them:

`\begin{aligned}f(-4)-f(1)&=(-(-4)^2+8(-4)-11)-(-(1)^2+8(1)-11)\\\\&=(-(16)-32-11)-(-(1)+8-11)\\\\&=(-16-32-11)-(-1+8-11)\\\\&=(-59)-(-4)\\\\&=-59+4\\\\&=-55\end{aligned}`

Question 17

To find g(9) + h(-14), substitute x = 9 into function g(x), and x = -14 into function h(x), then add them:

`\begin{aligned}g(9) + h(-14)&=\left(14-(2)/(3)(9)\right)+(-(-14)-7)\\\\&=\left(14-6\right)+(14-7)\\\\&=\left(8\right)+(7)\\\\&=8+7\\\\&=15\end{aligned}`

Question 18

To find h(8) - 2·f(3), substitute x = 8 into function h(x), and x = 3 into function f(x), multiply f(3) by 2, then subtract them:

`\begin{aligned}h(8) - 2 \cdot f(3)&=(-(8)-7)-2(-(3)^2+8(3)-11)\\\\&=(-8-7)-2(-(9)+24-11)\\\\&=(-15)-2(-9+24-11)\\\\&=(-15)-2(4)\\\\&=-15-8\\\\&=-23\end{aligned}`

Question 19

To find ¹/₂g(-6) + f(-2), substitute x = -6 into function g(x) then halve it, and x = -2 into function f(x), then add them:

`\begin{aligned}(1)/(2)g(-6)+f(-2)&=(1)/(2)\left(14-(2)/(3)(-6)\right)+(-(-2)^2+8(-2)-11)\\\\&=(1)/(2)\left(14-(-4)\right)+(-(4)-16-11)\\\\&=(1)/(2)\left(14+4\right)+(-4-16-11)\\\\&=(1)/(2)\left(18\right)+(-31)\\\\&=9-31\\\\&=-22\end{aligned}`