Suppose H(x) = radical(5-7x^2) . Find two functions and such that (f x g)(x) = H(x)

Answer 1

If it’s product of f(x) and g(x) think about factoring 5-7x²

5(1-(7x²)/5) then remember when you multiply radicals of the same power you just find the product and keep the radical.

So f(x) = sqrt 5

and g(x) = sqrt (1-(7/5)x²)

But if it’s (f o g)(x) then yes, it’s a composite function.

Mrs. S

Answer 2

I am guessing (fxg)(x) is a composite function (f*g)(x).

H(x) is the composite of two functions: √x and 5-7x²

5-7x² is the 'inside' function and √x is the 'outside' function. Can you figure out what f and g are? Let me know if you need more help!