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Find the inverse of the following and show your Solution

1. f(x)=2x-1

2. f(x)=4x-5

3. f(x)=3x-1

4. f(x)=3x+6

5. f(x)=3x​

Sagot :

Pisteeeidn

Answer:

1. f(x)=2x-1

y=2x-1

x=2y-1

2y-1=x

2y=x+1

[tex]y = \frac{1}{2} \times + \frac{1}{2} [/tex]

[tex]f {}^{ - 1} ( \times ) = \frac{1}{2} \times + \frac{1}{2} [/tex]

[tex]2. \: f(x) = 4 \times - 5[/tex]

[tex]y = 4 \times - 5[/tex]

[tex] \times = 4y - 5[/tex]

[tex]4y - 5 = x[/tex]

[tex]4y = \times + 5[/tex]

[tex]y = \frac{1}{4} \times + \frac{5}{4} [/tex]

[tex]f {}^{ - 1} (x) = \frac{1}{4} \times + \frac{5}{4} [/tex]

[tex]3. \: f(x) = 3 \times - 1[/tex]

[tex]y = 3 \times - 1[/tex]

[tex]x = 3y - 1[/tex]

[tex]3y - 1 = x[/tex]

[tex]3y = \times + 1[/tex]

[tex]y = \frac{1}{3} \times + \frac{1}{3} [/tex]

[tex]f {}^{ - 1} (x) = \frac{1}{3} \times + \frac{1}{3} [/tex]

[tex]4. \: f(x) = 3 \times + 6[/tex]

[tex]y = 3 \times + 6[/tex]

[tex]x = 3y + 6[/tex]

[tex]3y + 6 = x[/tex]

[tex]3y = x - 6[/tex]

[tex]y = \frac{1}{3} \times - 2 [/tex]

[tex]f {}^{ - 1} (x) = \frac{1}{3} x - 2[/tex]

[tex]5. \: f(x) = 3x[/tex]

[tex]y = 3x[/tex]

[tex]x = 3y[/tex]

[tex]3y = x[/tex]

[tex]y = \frac{1}{3} \times [/tex]

[tex]f {}^{ - 1} (x) = \frac{1}{3} x[/tex]