if-f-x-x-13-5-and-g-x-x-13-1-5-Which-one-is-correct-1-f-x-g-x-2-f-x-g-x-

Question Number 171318 by sciencestudent last updated on 12/Jun/22

i f f (x) = x^{\frac{13}{5}} a n d g (x) = \sqrt[5]{x^{13}}

W h i c h o n e i s c o r r e c t ?

1) f (x) = g (x) 2) f (x) \neq g (x)

Commented by mr W last updated on 12/Jun/22

x^{\frac{13}{5}} = \sqrt[5]{x^{13}}

Answered by mathlove last updated on 14/Jun/22

c h e k t h i s M r W

∴ f (x) = g (x) \Rightarrow D_{f} = D_{g} a n d R_{f} = R_{g}

D_{f} = [0, \infty) a n d D_{g} = R

D_{f} \neq D_{g} \Rightarrow f (x) \neq g (x)

Commented by mr W last updated on 14/Jun/22

{w h a t}^{'} s t h e d i f f e r e n c e b e t w e e n

x^{\frac{13}{5}} a n d \sqrt[5]{x^{13}} ? i f t h e y a r e d i f f e r e n t t o

y o u, t h e n x^{\frac{1}{3}} \neq \sqrt[3]{x} t o y o u t o o!

Commented by mathlove last updated on 15/Jun/22

i s {(- 3)}^{\frac{3}{2}} = ?

Commented by mathlove last updated on 15/Jun/22

{(- 3)}^{1} = - 3 \Rightarrow {(- 3)}^{\frac{2}{2}} = {({(- 3)}^{2})}^{\frac{1}{2}} = {(9)}^{\frac{1}{2}} = \sqrt{9} = 3

? - 3 = 3

Commented by mr W last updated on 15/Jun/22

i j u s t s a i d x^{\frac{13}{5}} = \sqrt[5]{x^{13}}, n o t h i n g e l s e!

d o y o u w a n t t o s a y : {(- 3)}^{\frac{3}{2}} {d o e s n}^{'} t

e x i s t, b u t \sqrt{{(- 3)}^{3}} e x i s t s ?

a g a i n : w h a t i s t h e d i f f e r e n c e b e t w e e n

f (x) = x^{\frac{13}{5}} a n d g (x) = \sqrt[5]{x^{13}} ?

Commented by mathlove last updated on 15/Jun/22

u n d e r s t a n d t h e y a r e b o t h e q u l e