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Functions and Graphs

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Question 61

The function fff is defined by f(x)=3x+5x−4,x≠4f(x) = \frac{3x + 5}{x - 4}, \quad x \neq 4f(x)=x−43x+5​,x=4

a.

Find f−1(x)f^{-1}(x)f−1(x).

[3]
b.

Show that ff(x)=ax+bcx+dff(x) = \frac{ax + b}{cx + d}ff(x)=cx+dax+b​ where a,b,ca, b, ca,b,c and ddd are integers to be found.

[3]
c.

The point P(5,20)P(5, 20)P(5,20) lies on the curve with equation y=f(x)y = f(x)y=f(x).

Find the point to which PPP is mapped when y=f(x)y = f(x)y=f(x) is transformed to the curve with equation y=3f(2x)−10y = 3f(2x) - 10y=3f(2x)−10.

[3]

Functions and Graphs Questions

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