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
`$f(2)=8$`

Step-by-step 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
`$f(2)=8$`