Question

The function f(x) is defined as follows: Determine the following values of the function. f(-3) = a0 and f(2) = a1 i

Answer 1

Question:

The function f(x) is defined as follows:

f(x)= 3x+1 if x is less than or equal to 0

2x^2 if 0 4 if c is greater than or equal to 2

determine the following values of the function

f(-3)= __

f(2)= ___

Answer:

The values are $f(-3)=-8$ and $f(2)=8$

Explanation:

The function is defined by two parts,

$f(x)=3 x+1$ if $x\leq 0$

$f(x)=2x^2$ if $x \geq 2$

To determine the value of $f(-3)$ , we shall substitute the value $x=-3$ in the function $f(x)=3 x+1$ because $-3 \leq 0$

Hence, we have,

$f(x) \ \ =3 x+1\\f(-3)=3(-3)+1\\f(-3)=-9+1\\f(-3)=-8$

Now, to determine the value of $f(2)$ , we shall substitute the value $x=2$ in the function $f(x)=2x^2$ because $x \geq 2$

Hence, we have,

$f(x)=2 x^{2}\\f(2)=2\left(2^{2}\right)\\f(2)=2(4)\\f(2)=8$

Thus, the values are $f(-3)=-8$ and $f(2)=8$