The inverse of the given function y =x+5 is y =x-5.
The given function is:
y =x+5
A function is invertible only if each input has a unique output and each element of the codomain should be mapped.
Step1: check function is invertible i.e. bijective i.e. one-one and onto or not
f(x₁)=x₁+5
f(x₂) = x₂+5
f(x₁) = f(x₂)
x₁+5 =x₁+5
x₁=x₂
So, the function is one-one or injective.
For onto range and codomain should be same.
Step 2: interchange x and y
x=y+5
Step3: bring 5 to the left side of the equation.
x-5 = y
Step4: write in y=f(x) form
y = x-5
Therefore, the inverse of the given function y =x+5 is y =x-5.
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