### Home > A2C > Chapter 1 > Lesson 1.1.2 > Problem1-22

1-22.

Given $f(x) = −\frac23x + 3$ and $g(x) = 2x^2 − 5$, complete parts (a) through (f) below.

1. Calculate $f(3)$.

Substitute $3$ for each $x$ in $f(x)$.

$f(3)=-\frac{2}{3}(3)+3$

Simplify.

1. Solve $f(x)=−5$.

Substitute $−5$ for $f(x)$.

$-5=-\frac{2}{3}x+3$

Subtract $3$ from both sides.

$-8=-\frac{2}{3}\textit{x}$

Get the $x$-term alone.

$\left(-\frac{3}{2}\right)(-8)=\left(-\frac{2}{3}x\right)\left(-\frac{3}{2}\right)$

$x=12$

1. Calculate $g(−3)$.

Substitute $−3$ for each $x$ in $g(x)$.

$g(−3)=2(−3)^2−5$

Simplify.

1. Solve $g(x)=9$.

Follow the same steps from part (a).

1. Solve $g(x)=8$.

Follow the same steps from part (b).

$x=\pm\sqrt\frac{13}{2}$

1. Solve $g(x)=−7$.

Follow the same method from part (c).

Use the eTool below to solve for each part.
Click the link at right for the full version of the eTool: A2C 1-22 HW eTool