Which of the following is a rational function?

\frac{1}{3} \sqrt{4 x^{3} + 4 x + 7}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{3 x^{3} - 7 x + 1}{x - 2}, x \neq 2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{3 x^{5} + 5 x^{3} + 2 x + 7}{x^{3 / 2}}, x > 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{\sqrt{1 + x}}{2 + 5 x}, x \neq - 2 / 5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D $\frac{3 x^{3} - 7 x + 1}{x - 2}, x \neq 2$
Only B is rational function because both nominator & denominator are rational.

In A, nominator $\sqrt{4 x^{3} + 4 x + 7}$ is irrational.

In C, denominator $x^{\frac{3}{2}}$ is irrational.

In D, nominator $\sqrt{1 + x}$ is irrational.

Suggest Corrections

Similar questions

Factorize $2 x^{2} - 7 x + 5 = 0$

Solve :

$(i) \frac{1}{3} x - 6 = \frac{5}{2} (i i) \frac{2 x}{3} - \frac{3 x}{8} = \frac{7}{12} (i i i) (x + 2) (x + 3) + (x - 3) (x - 2) - 2 x (x + 1) = 0 (i v) \frac{1}{10} - \frac{7}{x} = 35 (v) 13 (x - 4) - 3 (x - 9) - 4 (x + 4) = 0 (v i) x + 7 - \frac{8 x}{3} = \frac{17 x}{6} - \frac{5 x}{8} (v i i) \frac{3 x - 2}{4} - \frac{2 x + 3}{3} = \frac{2}{3} - x (v i i i) \frac{x + 2}{6} - (\frac{11 - x}{3} - \frac{1}{4}) = \frac{3 x - 4}{12} (i x) \frac{2}{5 x} - \frac{5}{3 x} = \frac{1}{15} (x) \frac{x + 2}{3} - \frac{x + 1}{5} = \frac{x - 3}{4} - 1 (x i) \frac{3 x - 2}{3} + \frac{2 x + 3}{2} = x + \frac{7}{6} (x i i) x - \frac{x - 1}{2} = 1 - \frac{x - 2}{3} (x i i i) \frac{9 x + 7}{2} - (x - \frac{x - 2}{7}) = 36 (x i v) \frac{6 x + 1}{2} + 1 = \frac{7 x - 3}{3}$

\int \frac{4 x^{5} - 7 x^{4} + 8 x^{3} - 2 x^{2} + 4 x - 7}{x^{2} (x^{2} + 1)^{2}} d x

Q. Solve the following equations:

\sqrt{2 x^{2} + 5 x - 7} + \sqrt{3 (x^{2} - 7 x + 6)} - \sqrt{7 x^{2} - 6 x - 1} = 0

Q. Read the following statements
(a)

x^{2} - 5 x + \sqrt{2}

is a polynomial in x.
(b)

4 x^{2} - 3 \sqrt{x} + 7

is not a polynomial in x.
(c)

\frac{x^{2} + 2 x + 5}{x + 3} (x \neq - 3)

is a rational expression.
(d)

\frac{x^{3} - 5 \sqrt{x} - 1}{x^{2} + x + 4}

is not a rational expression.
Correct options is -

Join BYJU'S Learning Program

Which of the following is a rational function?

The correct option is D 3x3−7x+1x−2,x≠2Only B is rational function because both nominator & denominator are rational.In A, nominator √4x3+4x+7 is irrational.In C, denominator x32 is irrational.In D, nominator √1+x is irrational.