You visited us 1 times! Enjoying our articles? Unlock Full Access!

Composite Function

If fx = 4x+...

Question

If $f (x) = 4 x + 2, g (x) = 3 x^{2}, h (x) = 3 x - 2$ such that $f o (g o h) = (f o g) o h$

Open in App

Solution

$f (x) = 4 x + 2, g (x) = 3 x^{2}, h (x) = 3 x - 2$
To show $f 0 (g 0 h) = (f 0 g) 0 h$
$L H S f 0 (g 0 h) = 3 {(3 x - 2)}^{2} f 0 (g 0 h) = 4 [3 {(3 x - 2)}^{2}] + 2 = 12 {(3 x - 2)}^{2} + 2 = 108 x^{2} - 144 x + 50 R H S f o g = 4 \times 3 x^{2} + 2 = 12 x^{2} + 2 (f 0 g) 0 h = 12 {(3 x - 2)}^{2} + 2 = 12 (9 x^{2} + 4 - 12 x) + 2 = 108 x^{2} - 144 x + 50$
Hence proved,
$f 0 (g 0 h) = (f 0 g) 0 h$

Suggest Corrections

Similar questions

f (x) = x + 2, g (x) = 2 x + 3, h (x) = 3 x^{4}

x ϵ R

f o (g o h)

f (x) = \frac{2}{x + 1}

g (x) = cos x

h (x) = \sqrt{x + 3}

(f o g o h)

\sqrt{x}

\frac{2}{3} x^{2} - \frac{7}{4} x + 9

\frac{4}{x}

x^{4} - x^{\frac{3}{2}} + x - 1

2 + \frac{3}{x} + 4 x

Identify polynomials in the following :

(i) f(x) = $4 x^{3} - x^{2}$ - 3x + 7

(ii) g(x) = $2 x^{3} - 3 x^{2} + \sqrt{x} - 1$

(iii) p(x) = $\frac{2}{7} x^{2} - \frac{7}{4} x + 9$

(iv) q(x) = $2 x^{2} - 3 x + \frac{4}{x} + 2$

(v) h(x) = $x^{4} - x^{\frac{3}{2}} + x - 1$

(vi) f(x) = 2 + $\frac{3}{x} + 4 x$

f (x) = 3 x - 1

g (x) = 4 x + 2

g (f (0) + 2)

Join BYJU'S Learning Program