Respuesta :
Answer:
Step-by-step explanation:
g
(
x
)
=
−
2
(
x
−
4
)
Replace
g
(
x
)
with
y
.
y
=
−
2
(
x
−
4
)
Interchange the variables.
x
=
−
2
(
y
−
4
)
Solve for
y
.
y
=
−
x
2
+
4
Solve for
y
and replace with
g
−
1
(
x
)
.
g
−
1
(
x
)
=
−
x
2
+
4g
(
x
)
=
−
2
(
x
−
4
)
Replace
g
(
x
)
with
y
.
y
=
−
2
(
x
−
4
)
Interchange the variables.
x
=
−
2
(
y
−
4
)
Solve for
y
.
Tap for more steps...
y
=
−
x
2
+
4
Solve for
y
and replace with
g
−
1
(
x
)
.
g
−
1
(
x
)
=
−
x
2
+
4
The inverse of the function G(X)=-2(x-4) is G'(x) = -(1/2)x +4
What is a Function?
A function is a law that relates a dependent and an independent variable.
The function is g(x) = -2(x-4)
The inverse of a function is found by interchanging the position of the x an d y variable and then solving for y in terms of x.
g(x) = -2 (x-4)
y = -2(x-4)
Interchanging y to x
x = -2( y-4)
x = -2y +8
(x - 8)/ -2 = y
y = 4 - (1/2)x
To know more about Function
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