Question

What are the answers to 6-7? Help!

Answer 1

Number 6 is {{{y=4x^3 - 7}}} solve for x
{{{4x^3=y+7}}}
{{{x^3=(y+7)/4}}}
{{{x=root(3,(y+7)/4)}}}
{{{f^(-1)=root(3,(x+7)




And Number 7 is Replace
f
(
x
)
f
(
x
)
with
y
y
.
y
=
3
x
x
+
2
y
=
3
x
x
+
2
Interchange the variables.
x
=
3
y
y
+
2
x
=
3
y
y
+
2
Solve for
y
y
.

f
−
1
(
x
)
=
−
2
x
x
−
3

Answer 2

6.) y = 3(4x+7)^(1/2)

Solve for x:
Square both sides:
y^2 = 9(4x+7)
y^2 = 36x + 63
y^2-63 = 36x
(y^2-63)/36 = x

Now swap x and y:
f^-1(x) = (x^2-63)/36

The above of the inverse function.  However we need to restrict the domain since it does not pass the vertical line test.  Since the original function has a range of y ≥ 0.  The domain of our inverse is x ≥ 0.

You are only allowed 1 question per post, so I won't do the second question.