The equation for inverse function g−1(x) for the function g(x)=x + 2.

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The equation for inverse function g−1(x) for the function g(x)=x + 2.

Pohanginah · Accepted Answer

Consider the function, g(x)=x+2. The function g(x)=x+2. it is the same function if x≥0andg(x)&amp;gt;0. In order to find the inverse of a function, first replzce g(x) by y. y=x+2 Now, interchange x and y, x=y+2 To simplify the above equation further, use the formula, if mx=n, then m=±nx, where n and m are positive real numbers, n ≠ 0 and x is the positive integer, x2=y + 2 y=x2 − 2 Thus, change y by g−1(x). g−1(x)=x2 − 2 for x≥0 Therefore, the inverse of the given function g(x)=x+2isg01(x)=x2−2 for x≥0 Use the transformation of the graph of the parent function h(x)=x to graph the given function g(x)=x+2. Draw the graph of the parent function h(x)=x. Plot the graph of h(x)=x  Consider the original function g(x)=x + 2. Use the properties of the transformation of the graph. In the graph of the function g(x)=x + 2the parent function gtaph h(x)=x is shifted to 2 unit towards the left along the abscissa. Hence, the grapg for the function g(x)=x + 2 is  Similarly, using the transformation of the graphs, plot the graph of the inverse function g−1(x)=x2 − 2 for the restriction x ≥ 0.  It can be observed that the curve of the inverse function g−1(x)=x2 − 2 for the restriction x ≥ 0 and the function g(x)=x + 2 are symmetric with respect to the line y=x.

The equation for inverse function g^{-1} (x) text{for the function} g (x) = sqrt{x + 2}.

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