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Standard XII

Mathematics

Differentiation of a Determinant

If f : R r...

Question

If f : R → R defined by f(x) = 3x − 4 is invertible, then write f⁻¹ (x).

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Solution

$Let f^{- 1} (x) = y . . . (1) \Rightarrow f (y) = x \Rightarrow 3 y - 4 = x \Rightarrow 3 y = x + 4 \Rightarrow y = \frac{x + 4}{3} \Rightarrow f^{- 1} (x) = \frac{x + 4}{3} [from (1)]$

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If f : R → R defined by f(x) = 3x − 4 is invertible, then write f⁻¹ (x).

$Let f^{- 1} (x) = y . . . (1) \Rightarrow f (y) = x \Rightarrow 3 y - 4 = x \Rightarrow 3 y = x + 4 \Rightarrow y = \frac{x + 4}{3} \Rightarrow f^{- 1} (x) = \frac{x + 4}{3} [from (1)]$

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If f : R → R defined by f(x) = 3x − 4 is invertible, then write f−1 (x).

Letf-1x=y...1⇒fy=x⇒3y-4=x⇒3y=x+4⇒y=x+43⇒f-1x=x+43[from1]

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If f : R → R defined by f(x) = 3x − 4 is invertible, then write f⁻¹ (x).

$Let f^{- 1} (x) = y . . . (1) \Rightarrow f (y) = x \Rightarrow 3 y - 4 = x \Rightarrow 3 y = x + 4 \Rightarrow y = \frac{x + 4}{3} \Rightarrow f^{- 1} (x) = \frac{x + 4}{3} [from (1)]$