For x ≥ 0, the value h(k(x)) is not equal to the value of k(h(x))
For x≥ 0, since h(k(x)) ≠ k(h(x)), then the functions h and k are not inverse function
Inverse functions
Given the following functions
h(x) = 5x^2 - 1
k(x) = √5x + 1
Determine the composite function h(k(x))
h(k(x)) = h(√5x +1)
h(k(x)) = 5(√5x +1)^2 - 1
h(k(x)) = 5(5x+1)-1
h(k(x)) = 25x + 5 -1
h(k(x) = 25x+4
Similarly for the function k(h(x))
k(h(x)) = k(5x^2-1)
k(h(x)) = √5(5x^2-1)^2+1
Hence we can conclude that for x ≥ 0, the value h(k(x)) is not equal to the value of k(h(x))
For x≥ 0, since h(k(x)) ≠ k(h(x)), then the functions h and k are not inverse function
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