Question

1. Find the inverse function of f(x)
c) f(x) = 3(x - 7) + 5​

Answer 1

Answer:

Let

y

=

f

(

x

)

and apply a sequence of operations to both sides of the equation to isolate

x

and find:

f

−

1

(

y

)

=

−

7

√

y

+

2

3

Explanation:

Let

y

=

f

(

x

)

=

−

3

x

7

−

2

Add

2

to both ends to get:

y

+

2

=

−

3

x

7

Divide both sides by

−

3

to get:

x

7

=

−

y

+

2

3

Take

7

th root to get:

x

=

7

√

−

y

+

2

3

=

−

7

√

y

+

2

3

(since

(

−

1

)

7

=

−

1

)

So

f

−

1

(

y

)

=

−

7

√

y

+

2

3

Answer 2

Answer:

we know y =f (x) =>x=f^(-1)(y)

y=f (x)=3 (x-7)+5

=>y=3x-21+5=3x-16

=>3x=y+16

x=(y+16)/3

${f}^{ - 1} (y) = \frac{y + 16}{3} \\ replace \: y \: by \: x \: then \: \\ {f}^{ - 1} (x) = \frac{x + 16}{3}$