Question

If f (x )equals left brace Start 2 By 1 Matrix 1st Row 1st Column 2 x minus 3 if minus 2 less than or equals x less than or equals 5 2nd Row 1st Column x cubed minus 5 if 5 less than x less than or equals 6 EndMatrixf(x)= 2x−3 if −2≤x≤5 x3−5 if 5

Answer 1

(a)f(0)=-3

(b)f(1)=-1

(c)f(5)=7

(d)f(6)=211

Explanation:

`f(x)=\left\{\begin{array}{ccc}2x-3, &-2\leq x \leq 5 \\x^3-5, &5<x\leq6 \end{array}\right`

(a) f(0)

For x such that ,
`-2\leq x \leq 5, f(x)=2x-3`

Since
`-2\leq 0\leq 5`

`f(0)=2(0)-3=0-3\\f(0)=-3`

(b)f(1)

For x such that ,
`-2\leq x \leq 5, f(x)=2x-3`

Since
`-2\leq 1\leq 5`

`f(1)=2(1)-3=2-3\\f(1)=-1`

(c)f(5)

For x such that ,
`-2\leq x \leq 5, f(x)=2x-3`

Since
`-2\leq 5\leq 5`

`f(5)=2(5)-3=10-3\\f(5)=7`

(d)f(6)

For x such that
`5<x\leq6, f(x)=x^3-5`

`f(6)=6^3-5\\f(6)=211`