Question

Given the function how do I solve

Answer 1

Answer: (a) -7 (b)
`\bold{(4)/(25)}` (c)
`\bold{-(5)/(2)}` (d) 4

Explanation:

A) f(x) = 2x - 3 when x is between -5 and -2 (including -5 and -2)

B) f(x) = x² when x is between -2 and 2 (including 2)

C)
`f(x)=-(3)/(2)x+(7)/(2)` when x is between 2 and 5 (including 5)

a) Equation A includes x = -2

f(x) = 2x - 3

f(-2) = 2(-2) - 3

= -4 - 3

= -7

b) Equation B includes x =
`-(2)/(5)`

f(x) = x²

`f\bigg(-(2)/(5)\bigg) = \bigg(-(2)/(5)\bigg)^2`

`=(4)/(25)`

c) Equation C includes x = 4

`f(x)=-(3)/(2)x+(7)/(2)`

`f(4)=-(3)/(2)(4)+(7)/(2)`

`=-(12)/(2)+(7)/(2)`

`=-(5)/(2)`

d) Try each equation to see if x falls within the values given.

A) f(x) = 2x - 3

-2.5 = 2x - 3

0.5 = 2x

0.25 = x NOT VALID since x should be between -5 and -2

B) f(x) = x²

-2.5 = x²

`√(-2.5)=x` NOT VALID since x cannot be an imaginary number

C)
`f(x)=-(3)/(2)x+(7)/(2)`

`-(5)/(2)=-(3)/(2)x+(7)/(2)`

`-(12)/(2)=-(3)/(2)x`

`-(12)/(2)\bigg((2)/(3)\bigg)=x`

`4 = x` VALID since x is between 2 and 5