Tip:A–D to answerE for explanationV for videoS to reveal answer
The graph of function f(x)=loge(x3+x6+1) is symmetric about
- A.
X-axis
- B.
Y-axis
- C.
Origin
(Correct Answer) - D.
Y = x
Explanation
f(x) = log(x³ + √(x⁶ + 1))
f(-x) = log[(−x)³ + √((−x)⁶ + 1)]
f(-x) = log[√(x⁶ + 1) − x³]
= log[(√(x⁶ + 1) − x³)(√(x⁶ + 1) + x³)]
= log[(√(x⁶ + 1) + x³)⁻¹]
= log[(x³ + √(x⁶ + 1)]⁻¹
= −log(x³ + √(x⁶ + 1))
= −f(x) Odd function
We should know that odd functions are symmetrical about origin.
Explanation
f(x) = log(x³ + √(x⁶ + 1))
f(-x) = log[(−x)³ + √((−x)⁶ + 1)]
f(-x) = log[√(x⁶ + 1) − x³]
= log[(√(x⁶ + 1) − x³)(√(x⁶ + 1) + x³)]
= log[(√(x⁶ + 1) + x³)⁻¹]
= log[(x³ + √(x⁶ + 1)]⁻¹
= −log(x³ + √(x⁶ + 1))
= −f(x) Odd function
We should know that odd functions are symmetrical about origin.
