Maths GCSE AQA HIGHER

Question

f(x)=2x/5 - 1

Work out the value of      f ^–1(3) + f(–0.5)

Answer 1

y=2x/5 - 1 to find the inverse function, switch x and y, and solve for y

x =2y/5 -1

2y/5 = x+1

y = (5/2)(x+1) = f^-1(x)

f^-1(3) = (5/2)(3+1) = (5/2)4 = 10

f^(.5) = 2(.5)/5 -1 = .2-1 =-.8

f^-1(3) + f^(.5) = 10 + (-.8) = 9.2