Question

Hell don’t understand homework If f(x)= 5x-1

Answer 1

Answer:

(a)  -1

(b)  4

(c)  14

(d)  61

Step-by-step explanation:

A piecewise function is a function which has different definitions for different intervals of x.

Given:

$f(x)=\begin{cases}5x-1 \quad \textsf{if }-5\leq x \leq 3\\x^3-3 \quad \textsf{if }\:\:\:\:\:\:3 < x \leq 4\end{cases}$

f(x) has 2 definitions:

Definition 1

$5x-1$ when x is more than or equal to -5 and less than or equal to 3.  This is a linear function.

Definition 2

$x^2-3$ when x is more than 3 and less than or equal to 4.  This is a cubic function.

Part (a)

We have to find f(0), so when x = 0.

x = 0 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

$f(x)=5x-1$

Substitute x = 0 in this definition:

$\implies f(0)=5(0)-1=-1$

Part (b)

We have to find f(1), so when x = 1.

x = 1 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

$f(x)=5x-1$

Substitute x = 1 in this definition:

$\implies f(0)=5(1)-1=4$

Part (c)

We have to find f(3), so when x = 3.

x = 3 satisfies the condition -5 ≤ x ≤ 3 so the corresponding function is

$f(x)=5x-1$

Substitute x = 3 in this definition:

$\implies f(0)=5(3)-1=14$

Part (d)

We have to find f(4), so when x = 4.

x = 4 satisfies the condition 3 < x ≤ 4 so the corresponding function is

$f(x)=x^3-3$

Substitute x = 4 in this definition:

$\implies f(4)=(4)^3-3=61$