How do you find the inverse of f(x)= -|x+1|+4f(x)=−|x+1|+4 and is it a function?

1 Answer
A. S. Adikesavan
Apr 17, 2016

x=+-|y-4|-1x=±|y−4|−1

Explanation:

y=f(x)<=4y=f(x)≤4
The given relation creates 2-1 mapping.. For a given y, there are two values of x, from the equivalent bifurcated equations
y=+-(x=1)+4y=±(x=1)+4

For the inverse, solve for x, from there equations.

x= 3-y=(4-y)-1 and x=-(4-y)-1x=3−y=(4−y)−1andx=−(4−y)−1

to be combined as

x= +-|y-4|-1x=±|y−4|−1

Care has been taken to prefix both signs to |y-4||y−4|, to include all x values, permitted by the given equation. This would combine both x>=-1x≥−1 (for + sign) and x<=-1x≤−1 (for - −sign).

Anyway, the graph is a ^^∧-like right angle at (-1, 4) that is bisected by x = -1.

Related questions
See all questions in Function Composition
Impact of this question
1613 views around the world
You can reuse this answer
Creative Commons License