Question

The answer is a=6 , b=-5. Can someone explain how to get thosse two anwers?​

Answer 1

The notation

h: x --> ax+b

is another way of saying h(x) = ax+b

The input is x, the output is h(x) = ax+b

The composite function notation h^2 is the same as (h o h)(x) or h(h(x)). I prefer h(h(x)) as it is the most descriptive of the three notation styles. The square notation is easily confused with actual squaring (when instead we want composite notation of a function with itself)

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h(x) = ax+b

h(x) = a( x )+b

h(h(x)) = a( h(x) )+b ... replace every x with h(x)

h(h(x)) = a( ax+b )+b .... replace the h(x) on the RHS with ax+b

h(h(x)) = a*ax + ab + b

h(h(x)) = a^2*x + (ab + b)

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Since h(h(x)) = 36x-35, this means we can equate the two expressions to find a and b

a^2*x + (ab+b) = 36x-35

we see that

a^2 = 36, so a = 6 (keep in mind a > 0)

since a = 6, we know that

ab+b = -35

6b+b = -35

7b = -35

b = -35/7

b = -5