Answer:
The inverse function of h(x) = 3/2*(X-11) is: g(x)= (2/3*X) +11
Step-by-step explanation:
h(x) = Y= 3/2*(X-11)
To find the inverse function, the first step is to exchange the position of the variables with each other. So;
X= 3/2*(Y-11)
Now we need to isolate the variable Y from this equation. The final result will be te inverse function.
X=3/2*(Y-11)
2*X=3*(Y-11)
2/3*X=Y-11
2/3*X +11 = Y
Y= (2/3*X) + 11 (Inverse function)
Answer:
[tex]h^{-1}(x)=\frac{2}{3}x+11[/tex]
Step-by-step explanation:
The given function is
[tex]h(x)=\dfrac{3}{2}(x-11)[/tex]
We need to find the inverse of the given function.
Step 1: Substitute h(x)=y.
[tex]y=\dfrac{3}{2}(x-11)[/tex]
Step 2: Interchange x and y.
[tex]x=\dfrac{3}{2}(y-11)[/tex]
Step 3: Isolate y.
[tex]\frac{2}{3}x=y-11[/tex]
[tex]\frac{2}{3}x+11=y[/tex]
Step 4: Interchange sides.
[tex]y=\frac{2}{3}x+11[/tex]
Step 5: Substitute [tex]y=h^{-1}(x)[/tex].
[tex]h^{-1}(x)=\frac{2}{3}x+11[/tex]
Therefore, the inverse of the function is [tex]h^{-1}(x)=\frac{2}{3}x+11[/tex].
