Simplify the following power functions to the form y=kxp, where k and p are some numbers.
(a) y=(18)/x√ is y=kxp. What are k and p?
y = 18/√x = 18x^(1/2)
y = √(18/x) = 3√2 x^(1/2)
Hard to tell what you meant, with that trailing √ sign.
Do you write 2x+ to mean 2+x as well?
To simplify the power function y = (18) / x√ into the form y = kxp, we need to rewrite the given function by expressing the power as a rational exponent.
First, we can rewrite x√ as x^(1/2).
Now we have y = (18) / x^(1/2).
To simplify it further, we can rewrite the expression in the denominator as a positive exponent: y = (18) * x^(-1/2).
Comparing this with the form y = kxp, we can see that k = 18 and p = -1/2.
So, y = (18) / x√ can be simplified to y = 18x^(-1/2), where k = 18 and p = -1/2.
To simplify the given power function y = (18)/(x√) into the form y = kx^p, where k and p are some numbers, we need to rationalize the denominator.
First, let's rewrite the function as:
y = 18/(√(x))
To rationalize the denominator, we'll multiply the numerator and denominator by the conjugate of the denominator (√(x)):
y = (18/(√(x))) * (√(x))/(√(x))
This simplifies to:
y = (18√(x))/x
Now, we can rewrite the function using fractional exponents:
y = 18x^(1/2) / x
To simplify this further, we can divide 18 by x:
y = 18x^(1/2-1)
Simplifying the exponent:
y = 18x^(-1/2)
Finally, rewriting the expression in the form y = kx^p, we have:
y = 18x^(-1/2) = 18/x^(1/2) = kx^p
In this case, k = 18 and p = -1/2.