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mllewestblam2

mllewestblam2

Answered question

2022-06-04

g ( x ) = 1 x 2 + 5 ( x > 2 )
Find the inverse function g 1 specifying the rule domain and image set.

Answer & Explanation

snowbargerpgl1f

snowbargerpgl1f

Beginner2022-06-05Added 3 answers

x subtract 2 x 2 take reciprocal 1 x 2 add 5 1 x 2 + 5
What gets done last gets undone first:
1 y 5 + 2   add 2   1 y 5   take reciprocal   y 5   subtract 5   y
so
g 1 ( y ) = 1 y 5 + 2.
trojanman849089tck

trojanman849089tck

Beginner2022-06-06Added 1 answers

Note that
g ( x ) = 1 x 2 + 5 = y 1 x 2 = y 5 x 2 = 1 y 5 x = 1 y 5 + 2
hence
g 1 ( y ) = 1 y 5 + 2
Now
x > 2 1 y 5 > 0 y > 5

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