Question

2-75. if $g(x)=x^2 - 5$, find the value(s) of $x$ so that:
a. $g(x)=20$
b. $g(x)=6$

Explanation:

Step1: Substitute $g(x)=20$

$20 = x^2 - 5$

Step2: Isolate $x^2$

$x^2 = 20 + 5 = 25$

Step3: Solve for $x$

$x = \pm\sqrt{25} = \pm5$

Step4: Substitute $g(x)=6$

$6 = x^2 - 5$

Step5: Isolate $x^2$

$x^2 = 6 + 5 = 11$

Step6: Solve for $x$

$x = \pm\sqrt{11}$

Answer:

a. $x=5$ and $x=-5$
b. $x=\sqrt{11}$ and $x=-\sqrt{11}$