What is the inverse of the function f(x) = x +3? h(x) = one-thirdx + 3 h(x) = one-thirdx – 3 h(x) = x – 3 h(x) = x + 34
Answers
Answer:
To find f^{-1}(y)f
−1
(y)f, start superscript, minus, 1, end superscript, left parenthesis, y, right parenthesis, we can find the input of fff that corresponds to an output of yyy. This is because if f^{-1}(y)=xf
−1
(y)=xf, start superscript, minus, 1, end superscript, left parenthesis, y, right parenthesis, equals, x then by definition of inverses, f(x)=yf(x)=yf, left parenthesis, x, right parenthesis, equals, y.
\begin{aligned} f(x) &= 3 x+2\\\\ y &= 3 x+2 &&\small{\gray{\text{Let f(x)=y}}} \\\\y-2&=3x &&\small{\gray{\text{Subtract 2 from both sides}}}\\\\ \dfrac{y-2}{3}&=x &&\small{\gray{\text{Divide both sides by 3}}} \end{aligned}
f(x)
y
y−2
3
y−2
=3x+2
=3x+2
=3x
=x
Let f(x)=y
Subtract 2 from both sides
Divide both sides by 3
So f^{-1}(y)=\dfrac{y-2}{3}f
−1
(y)=
3
y−2
f, start superscript, minus, 1, end superscript, left parenthesis, y, right parenthesis, equals, start fraction, y, minus, 2, divided by, 3, end fraction.
Since the choice of the variable is arbitrary, we can write this as f^{-1}(x)=\dfrac{x-2}{3}f
−1
(x)=
3
x−2
f, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 2, divided by, 3, end fraction.
Answer:
h(x) = 3x - 6
Step-by-step explanation:
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