Let f- g- - be defined by fx-2 x-1 and gx-x2-2 for all x - respectively- Then- find gof- -NCERT EXEMPLAR-

We have, nbsp;f, nbsp;g nbsp;: nbsp;R nbsp; #8594; nbsp;R nbsp;are defined by nbsp;f(x) = 2x nbsp;+ l and nbsp;g(x) = nbsp;x2 nbsp; ...

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Standard XII

Mathematics

Differentiation of a Determinant

Let f, g: 𝐑→...

Question

Let f, g : R $\to$ R be defined by f(x) = 2x + l and g(x) = x² $-$ 2 for all x $\in$ R, respectively. Then, find gof. [NCERT EXEMPLAR]

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Solution

We have,

f, g : R $\to$ R are defined by f(x) = 2x + l and g(x) = x² $-$ 2 for all x $\in$ R, respectively

$Now, g o f (x) = g (f (x)) = g (2 x + 1) = {(2 x + 1)}^{2} - 2 = 4 x^{2} + 4 x + 1 - 2 = 4 x^{2} + 4 x - 1$

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Let f, g : R → R be defined by f(x) = 2x + l and g(x) = x2 - 2 for all x ∈ R, respectively. Then, find gof. [NCERT EXEMPLAR]

We have, f, g : R → R are defined by f(x) = 2x + l and g(x) = x2 - 2 for all x ∈ R, respectively Now,gofx=gfx=g2x+1=2x+12-2=4x2+4x+1-2=4x2+4x-1

Let f, g : R $\to$ R be defined by f(x) = 2x + l and g(x) = x² $-$ 2 for all x $\in$ R, respectively. Then, find gof. [NCERT EXEMPLAR]

We have,

f, g : R $\to$ R are defined by f(x) = 2x + l and g(x) = x² $-$ 2 for all x $\in$ R, respectively

$Now, g o f (x) = g (f (x)) = g (2 x + 1) = {(2 x + 1)}^{2} - 2 = 4 x^{2} + 4 x + 1 - 2 = 4 x^{2} + 4 x - 1$