Respuesta :
Answer:
The inverse of the function h(x) is [tex]h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}[/tex].
Step-by-step explanation:
The given function is
[tex]h(x)=\dfrac{5}{2}x+4[/tex]
Replace h(x) by y.
[tex]y=\dfrac{5}{2}x+4[/tex]
Interchange x and y.
[tex]x=\dfrac{5}{2}y+4[/tex]
Subtract 4 from both sides to isolate variable y,
[tex]x-4=\dfrac{5}{2}y[/tex]
Multiply both sides by 2.
[tex]2x-8=5y[/tex]
Divide both sides by 5.
[tex]\frac{2}{5}x-\frac{8}{5}=y[/tex]
Replace y by h⁻¹(x).
[tex]h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}[/tex]
Therefore the inverse of the function h(x) is [tex]h^{-1}(x)=\frac{2}{5}x-\frac{8}{5}[/tex].
