Question

Which of the following statements have the same result? Explain each step in solving each one.. .

I f(3) when f(x) = 3x + 2.
II f-1(4) when f(x) = 2x minus 7, all over 3.
III 2y + 14 = 4y - 2
PLZ Explain...….

Answer 1

None, because
`11\\eq 9.5\\eq 8.`

Explanation:

I. When
`f(x)=3x+2,` then

`f(3)=3\cdot 3+2=9+2=11.`

II. Find the inverse function
`f^(-1)(x)` for the function
`f(x)=(2x-7)/(3).`

`y=(2x-7)/(3),\\ \\3y=2x-7,\\ \\2x=3y+7,\\ \\x=(3y+7)/(2),\\ \\f^(-1)(x)=(3x+7)/(2).`

Thus,

`f^(-1)(4)=(3\cdot 4+7)/(2)=(12+7)/(2)=(19)/(2)=9.5.`

III. Solve the equation
`2y+14=4y-2:`

`14+2=4y-2y,\\ \\16=2y,\\ \\y=16:2=8.`