Confirm that f and g are inverses by showing that f (g (x)) = x and g (f (x)) = x. f (x) = the quantity x minus seven divided by the quantity x plus three. and g (x) = quantity negative three x minus seven divided by quantity x minus one.

Question

Mathematics

Lilliana

1 April, 22:53

Confirm that f and g are inverses by showing that f (g (x)) = x and g (f (x)) = x. f (x) = the quantity x minus seven divided by the quantity x plus three. and g (x) = quantity negative three x minus seven divided by quantity x minus one.

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Waller · Answer 1

F (x) = (x-7) / (x+3)

g (x) = (-3x - 7) / (x-1)

f (g (x)) = (g (x) - 7) / (g (x) + 3)

= ((-3x - 7) / (x-1) - 7) / ((-3x - 7) / (x-1) + 3)

= ((-3x - 7) / (x-1) - 7 (x-1) / (x-1)) / ((-3x - 7) / (x-1) + 3 (x-1) / (x-1))

= ((-3x - 7) - 7 (x-1)) / ((-3x - 7) + 3 (x-1))

= (-3x - 7 - 7x + 7) / (-3x - 7 + 3x - 3)

= - 10x / (-10) = x ... proved

now your turn for g (f (x))