Question

Find gof and fog, if
$f(x)=8x^{3}\\g(x)= x^{\frac{1}{3} }$

Answer 1

Gɪᴠᴇɴ :-

• f(x) = 8x³
• g(x) = x^(1/3)

Tᴏ Fɪɴᴅ :-

• gof .
• fog.

Sᴏʟᴜᴛɪᴏɴ :-

❶ gof :-

→ g(x) = x^(1/3)

→ g[f(x)] = [f(x)]^(1/3)

→ gof(x) = (8x³)^(1/3)

→ gof(x) = [(2x)³]^(1/3)

→ gof(x) = (2x)^(3 * 1/3) { using (a^b)^c = (a)^(b*c) }.

→ gof(x) = 2x (Ans.)

___________________

❷ fog :-

→ f(x) = 8x³

→ f[g(x)] = 8[g(x)]³

→ fog(x) = 8[x^(1/3)]³

→ fog(x) = 8(x)^(1/3 * 3)

→ fog(x) = 8 * x

→ fog(x) = 8x (Ans.)

___________________

Answer 2

$\rule{200}3$

$\huge\tt{GIVEN:}$

• $f(x)=8x^{3}\\g(x)= x^{\frac{1}{3} }$

$\rule{200}2$

$\huge\tt{TO~FIND:}$

• Find gof & fog

$\rule{200}2$

$\huge\tt{SOLUTION:}$

GOF =

↪g(x) = x^(1/3)

↪g[f(x)] = [f(x)]^(1/3)

↪ gof(x) = (8x³)^(1/3)

↪gof(x) = [(2x)³]^(1/3)

↪gof(x) = (2x)^(3 × 1/3) { using (a^b)^c = (a)^(b×c) }.

↪ gof(x) = 2x

$\rule{200}1$

FOG =

↪f(x) = 8x³

↪f[g(x)] = 8[g(x)]³

↪fog(x) = 8[x^(1/3)]³

↪fog(x) = 8(x)^(1/3 * 3)

↪fog(x) = 8 × x

↪ fog(x) = 8x

$\rule{200}3$