Let y=f(x)=(3x+7)/(x-2) find a rule for f^-1

Mathematics

1 answer:

Murrr4er [49]3 years ago

8 0

Answer:

$f^{-1}(x)=\frac{2x+7}{x-3}$ .

Step-by-step explanation:

The given function is $f(x)=\frac{3x+7}{x-2},\:x\ne2$ .

We want to find a rule for $f^{-1}(x)$ .

Let $y=\frac{3x+7}{x-2}$ .

Interchange x and y.

$x=\frac{3y+7}{y-2}$ .

Solve for y.

$x(y-2)=3y+7$ .

Expand

$xy-2x=3y+7$ .

Group y-terms

$xy-3y=7+2x$ .

Factor

$(x-3)y=7+2x$ .

$y=\frac{2x+7}{x-3}$ .

$\therefore f^{-1}(x)=\frac{2x+7}{x-3},\:x\ne3$ .

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HELP ASAP!! Identify the matrix transformation of ΔPQR, which has coordinates P(−5, −2),Q(−6, −3), and R(−2, −3), for reflection

podryga [215]

Answer:

Matrix transformation = $\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]$

Vertices of the new image: P'= (5,-2), Q'= (6,-3), R'= (2,-3)

Step-by-step explanation:

Transformation by reflection will produce a new congruent object in different coordinate. Reflection to y-axis made by multiplying the x coordinate with -1 and keep the y coordinate unchanged. The matrix transformation for reflection across y-axis should be: $\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]$ .

To find the coordinate of the vertices after transformation, you have to multiply the vertices with the matrix. The calculation of the each vertice will be:

P'= $\left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]$ $\left[\begin{array}{ccc}-5\\-2\end{array}\right]$ = (5,-2)