Question

Suppose that the function f is defined. , for all real numbers, as follows.

Answer 1

Answer:   The values of......

$f(-5)=\frac{9}{4}\\ \\ f(-2)= -1\\ \\ f(4)=0$

Step-by-step explanation:

Given function is:   $\left \{ {{f(x)= \frac{1}{4}x^2 -4, if x\neq -2} \atop {=-1, if x=-2}} \right.$

For $f(-5),$  the value of $x$ is -5, which is not equal to -2.

So,  $f(-5)= \frac{1}{4}(-5)^2 -4 = \frac{1}{4}(25)-4 =\frac{25}{4}-4=\frac{25-16}{4}=\frac{9}{4}$

For $f(-2),$  the value of $x$ is -2.

So,  $f(-2)= -1$

For $f(4),$  the value of $x$ is 4, which is not equal to -2.

So,  $f(4)=\frac{1}{4}(4)^2 -4 =\frac{1}{4}(16)-4 =4-4=0$