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

Answer:

None, because $11\neq 9.5\neq 8.$

Step-by-step 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 $f(x)=\dfrac{2x-7}{3}.$

$y=\dfrac{2x-7}{3},\\ \\3y=2x-7,\\ \\2x=3y+7,\\ \\x=\dfrac{3y+7}{2},\\ \\f^{-1}(x)=\dfrac{3x+7}{2}.$

Thus,

$f^{-1}(4)=\dfrac{3\cdot 4+7}{2}=\dfrac{12+7}{2}=\dfrac{19}{2}=9.5.$

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

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