Which equation is the inverse of y = x2 + 16? y = x2 – 16 y = plus-or-minus StartRoot x EndRoot minus 16 y = plus-or-minus StartRoot x minus 16 EndRoot y = x2 – 4

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isyllus isyllus · Answer 1 · 2020-07-06T03:21:17+02:00

Answer:

[tex]\pm \sqrt{x-16}[/tex] is the inverse of [tex]y = x^2 + 16[/tex]

Step-by-step explanation:

Given that:

[tex]y = x^2 + 16[/tex]

Let us proceed step by step to calculate the inverse:

Step 1: Put [tex]y = f(x)[/tex]

[tex]f(x) = y=x^2 + 16[/tex]

Step 2: Interchange [tex]x[/tex] and [tex]y[/tex]:

[tex]x = y^2 + 16[/tex]

Step 3: Solve the equation to find the value of [tex]y[/tex]:

[tex]y^2 =x- 16\\\Rightarrow y =\pm \sqrt{x- 16}[/tex]

Step 4: Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:

[tex]\Rightarrow y =f^{-1}(x)=\pm \sqrt{x- 16}[/tex]

So, the inverse of [tex]y = x^2 + 16[/tex] is [tex]\pm \sqrt{x- 16}[/tex].

adioabiola adioabiola · Answer 2 · 2021-12-22T15:26:59+01:00

The equation which is the inverse of y = x2 + 16 is; f-¹ = y = ±√(x -16)

To evaluate the inverse of the function, y = x2 + 16.

We must first make x the subject of the formula and swap x and y as follows;

Therefore, the inverse function is;