Determine the inverse of f(x) = x^3 - x^2 - 2x show steps

Mathematics

1 answer:

ki77a [65]4 years ago

8 0

Switch the x and y values to find the inverse.

y=x−3x+2

The inverse is given by

x=y−3y+2

Solve for y now:

x(y+2)=y−3

xy+2x=y−3

2x+3=y−xy

2x+3=y(1−x)

2x+31−x=y

The inverse, f−1(x), is given by f−1(x)=2x+31−x.

The function can be graphed using knowledge of asymptotes, invariant points, and intercepts. Prepare a table of values for f(x). Recall that f−1(x) is simply a transformation of(x) over the line y=x, so f−1(x) has a table of values where X and y are inverted relative to f(x).

For example, if the point (2,3) belongs on the graph of f(x), the point (3,2) belongs on f−1(x).

Replace F(X)FX with yy.y=X3+2X−3Xy=X3+2X-3XInterchange the variables.X=y3+2y−3yX=y3+2y-3y

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Find the values of x for which the combined function h(x) = is undefined if f(x) = 5x + 1 and g(x) = x2 - 9.

Rama09 [41]

We need to know the definition of the "combined function" h(x). I'm going to guess--by looking at answers--that the function is $h(x)=\frac{f(x)}{g(x)}$ making it

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This function is undefined wherever the denominator is equal to 0 (division by zero is undefined). Factor the denominator.

$h(x)=\frac{5x+1}{(x+3)(x-3)}$

The two values of x that make the denominator 0 are 3 and -3, otherwise written $x=\pm 3$ .