Answer:6) y = x^(5/3)7) B8) C10) AStep-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))³f(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) + 8Switch the x and y and solve for y:x = 2√(y − 4) + 8x − 8 = 2√(y − 4)(x − 8) / 2 = √(y − 4)(x − 8)² / 4 = y − 4(x² − 16x + 64) / 4 = y − 4¼x² − 4x + 16 = y − 4y = ¼x² − 4x + 208) Find the inverse:x = 5√(y + 3) − 2x + 2 = 5√(y + 3)(x + 2) / 5 = √(y + 3)(x + 2)² / 25 = y + 3y = -3 + (x + 2)² / 25The inverse function is an upwards parabola with a vertex at (-2, -3). The best fit is C.desmos.com/calculator/fbabg5wc8b10) √(4x − 31) = x − 7Square both sides:4x − 31 = (x − 7)²4x − 31 = x² − 14x + 49Combine like terms:0 = x² − 18x + 80Factor:0 = (x − 8) (x − 10)x = 8 or 10Check for extraneous solutions.√(4×8 − 31) = 8 − 71 = 1√(4×10 − 31) = 10 − 73 = 3x = 8 and x = 10 are both solutions.