3. Name the type of functions for each.
a) g(x) =(3√(sin x))-8^3
b) h(t) = (3t^3 -7)/(√(x+2))
I would call no(1) a trigonometric function
And (Q2) a rational function......
Provided that x≠-2 for Question 2
actually, Q1 and Q2 suffer from the same problem. Rational functions are p(x)/q(x) where p and q are polynomials, not square roots of polynomials.
So, while Q1 involves a trigonometric function, g(x) is not actually a trig function. it is a function of a trig function, just as h(x) is a function of a rational function.
Quick question what would rather call h(t)???
Aaaaah spotted it already last line....thanks
a) The function g(x) can be described as a composition of three different types of functions. Let's break it down step by step:
1. The sine function: The function sin(x) is a trigonometric function that calculates the sine of an angle x. This function operates on the input x.
2. The cube root function: The function ∛(sin x) calculates the cube root of the result obtained from the sine function. The cube root is a type of radical function, also known as the third root.
3. The power function: The function 8^3 raises the number 8 to the power of 3. This is a power function that takes the number 8 as the base and 3 as the exponent.
So, the function g(x) can be categorized as a composition of a trigonometric function, followed by a radical function, and finally a power function.
b) The function h(t) also consists of two different types of functions. Let's go through each step:
1. The cubic function: The function 3t^3 is a polynomial function with a degree of 3. It involves raising the variable t to the power of 3 and then multiplying it by 3.
2. The reciprocal function: The function 1/(√(x+2)) is a reciprocal function, as it takes the reciprocal of the square root of the expression x+2.
So, the function h(t) can be categorized as a composition of a cubic function and a reciprocal function.