Which of the following expressions are identical? How do you figure it out?

Question

A) (sinx)^-1
B) arcsinx
C) sinx^-1
D) 1/sinx

Answer 1

A = 1/(sinx)
B = arcsin(x)
C = sin(1/x)
D = 1/(sinx)

A and D are the same.

By convention, the arcsin of x is written "sin^-1(x)", i.e. the -1 exponent on the word "sin," not on x. A and C could be mistaken for that, but they don't have the exponent in the right place.

(C) is the sine of 1/x because the exponent is performed before the sine operation.

Answer 2

Hey there!

Let's write the choices.

A. (sin(x))^-1.
B.arcsin(x).
C.sin(x^-1).
D.1/sin(x).

(sin(x))^-1 is not the same as arcsin(x). However, (sin(x))^-1 is equivalent to 1/sin(x), by the definition of negative exponent.

So the answers are A and D.

An inverse of the function is NOT the same as the recriprocal of the function i.e.

Let g(x) be the inverse of f(x). Then the following is false.

g(x)=1/f(x), this is false.

The correct answer would be.

g(x)≠1/f(x).

Let f(x)=sin(x), and g(x) be the inverse of f(x), i.e. g(x)=arcsin(x).

Here's the proof on why the statement is false.

g(x)=1/f(x).
arcsin(x)=1/sin(x).
arcsin(x)=csc(x), false.

See the proof?

Overall the choices are A and D. For B, the proof was mentioned above. For C, sin(x^-1), can be rewritten as sin(1/x).

Hope it helps!

Answer 3

A and D
a^-1 = 1/a
So (sinx)^-1 = 1/ sinx

Answer 4

A and c and D are identical. You can't figure it out. You just have to know it from having learned it.

Answer 5

a) and d)

anything to the negative exponent is equal to its reciprical to the positive exponent

Answer 6

(A & (D) ANS