Question

Math help pls, thank you! show steps if needed

Answer 1

Answer:

6) y = x^(5/3)

7) B

8) C

10) A

Step-by-step explanation:

6) The fifth root is the same as raising to the 1/5 power, so we can write this in exponent form as:

f(x) = (x^(1/5))³

f(x) = x^(3/5)

To find the inverse, switch x and y and solve for y.

x = y^(3/5)

y = x^(5/3)

7) f(x) = 2√(x − 4) + 8

Switch the x and y and solve for y:

x = 2√(y − 4) + 8

x − 8 = 2√(y − 4)

(x − 8) / 2 = √(y − 4)

(x − 8)² / 4 = y − 4

(x² − 16x + 64) / 4 = y − 4

¼x² − 4x + 16 = y − 4

y = ¼x² − 4x + 20

8) Find the inverse:

x = 5√(y + 3) − 2

x + 2 = 5√(y + 3)

(x + 2) / 5 = √(y + 3)

(x + 2)² / 25 = y + 3

y = -3 + (x + 2)² / 25

The inverse function is an upwards parabola with a vertex at (-2, -3).  The best fit is C.

desmos.com/calculator/fbabg5wc8b

10) √(4x − 31) = x − 7

Square both sides:

4x − 31 = (x − 7)²

4x − 31 = x² − 14x + 49

Combine like terms:

0 = x² − 18x + 80

Factor:

0 = (x − 8) (x − 10)

x = 8 or 10

Check for extraneous solutions.

√(4×8 − 31) = 8 − 7

1 = 1

√(4×10 − 31) = 10 − 7

3 = 3

x = 8 and x = 10 are both solutions.