The function g(h(x)) as an expression in terms of x is g(h(x)) = (x² - 1)(x² - 7)
How to write g(h(x)) as an expression in terms of x?
The functions are given as
g(x) = x² - 6x
h(x) = x² - 1
Recall that
g(x) = x² - 6x
Substitute h(x) for x in g(x) = x² - 6x
g(h(x)) = (h(x))² - 6(h(x))
Substitute h(x) = x² - 1 in g(h(x)) = (h(x))² - 6(h(x))
g(h(x)) = (x² - 1)² - 6(x² - 1)
Factor out (x² - 1)
g(h(x)) = (x² - 1)(x² - 1 - 6)
Evaluate the like terms
g(h(x)) = (x² - 1)(x² - 7)
Hence, the function g(h(x)) as an expression in terms of x is g(h(x)) = (x² - 1)(x² - 7)
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