f(x) is a linear function. If f(1) = 2 and f(3) = 8, then f(x) = .

3x - 1

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2x + 1

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3x + 1

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Solution

The correct option is A 3x - 1
Given: f(x) is a linear function.
f(1) = 2 and f(3) = 8

Let f(x) = ax + b
For x = 1,
f(1) = a + b
a + b = 2 ... (i)

For x = 3,
f(3) = 3a + b
3a + b = 8 ... (ii)
Subtract equation (i) from equation (ii)
2a = 6
a = 3
Put the value of a in equation (i)
3 + b = 2
b = -1
Put the values of a and b in f(x) = ax + b
f(x) = 3x -1

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