The x-intercept of the function are (√2-1,0) and(-√2-1,0). and the y-intercept of the function is (0,-1) and the inverse of the function is f⁻¹(x)=±√(x+2)-1.
The x and y intercepts of a function is defined as the points on the cartesian plane where the graph of the function intersects the co-ordinate axes.
The intercepts are calculated by substituting the value of x and y to zero to calculate the corresponding variable.
The inverse of a function y=g(x) is calculated by finding the value of x from the equation.
At x=0 , we get the y intercept.
f(0)=(0+1)²-2
or, f(0)=-1
So the y-intercept is at (0,-1) .
At y=0 we get the x-intercept.
f(x)=0
or,(x+1)²-2=0
or,(x+1)²=2
or, x+1= ±√2
or, x=±√2-1
Therefore the x-intercepts are (√2-1,0) and(-√2-1,0).
Now let us calculate the inverse of the function.
y=(x+1)²-2
or,y+2=(x+1)²
or, x+1=±√(y+2)
or, x=±√(y+2)-1
Hence the inverse of the function is written as
f⁻¹(x)=±√(x+2)-1
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