What is the range of f(x)=(7x+8)/(4x-7) ?

The range of f(x)=(7x+8)/(4x-7) is f(x) 7/4

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range of f(x)=(7x+8)/(4x-7)

range

f (x) = \frac{7 x + 8}{4 x - 7}

f (x) < \frac{7}{4} or f (x) > \frac{7}{4}

Interval Notation

(- \infty, \frac{7}{4}) \cup (\frac{7}{4}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{7 x + 8}{4 x - 7}

Inverse of

\frac{7 x + 8}{4 x - 7} : \frac{8 + 7 x}{4 x - 7}

\frac{8 + 7 x}{4 x - 7}

Find the domain of each inverse function

Domain of

\frac{8 + 7 x}{4 x - 7} : x < \frac{7}{4} or x > \frac{7}{4}

Combine the intervals

f (x) < \frac{7}{4} or f (x) > \frac{7}{4}

What is the range of f(x)=(7x+8)/(4x-7) ?
The range of f(x)=(7x+8)/(4x-7) is f(x)< 7/4 \lor f(x)> 7/4