Math

posted by .

Determine the range of each function
a)f(x)=(x^2+3)^2,XER
Answer is f(x)ER, f(x)>9
b)f(x)=1/3+x^4,XER
Answer is f(x)ER, 0<f(x)<1/3

Please explain how they go those two answers

  • Math -

    x^2+3 >= 3 for all x
    so, f(x) >= 9

    3+x^4 >= 3 for all x
    1/(3+x^4) <= 1/3 for all x
    as x gets huge, 1/x^4 -> 0 so,
    0 < f(x) <= 1/3

    wolframalpha.com will graph them for you to see

  • Math -

    I suppose that "XER" means the domain (all possible values of x) is all real numbers. And the answers there are both...wrong.
    Anyway, range is the set of all possible values of y (or f(x)). Let's analyze each problem. :)

    a) f(x) = (x^2+3)^2
    Note that x^2 can never be negative, because any real number squared is always greater than or equal to zero. Thus the smallest possible value of x^2 is zero, and if we substitute it in f(x),
    f(x) = (0^2 + 3)^2
    f(x) = 3^2
    f(x) = 9, which is the smallest possible value of f(x)
    Thus the range is all real numbers greater than or equal to 9, or f(x) >= 9

    b) f(x) = 1/3+x^4
    x^4 is also (x^2)^2. Then again, x^4 can never be negative. So the smallest possible value of x^4 is zero, and substituting,
    f(x) = (1/3) + 0^4
    f(x) = 1/3
    Thus the range is all real numbers greater than or equal to 1/3, or f(x) >= 1/3

    Hope this helps~ :3

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    g(x)=3 sin x domain and range is the domain: {xER} range {yEr|3< or = y}?
  2. math

    g(x)=3 sin x domain and range is the domain: {xER} range {yEr|3< or = y}?
  3. Math !!!!!

    a function f(x)has doamin {xeR/x>-4} and range {yeR/y<-1) . Determine the domain and range for each function. a) y=2f(x) b) y=f(-x) c) y=3f(x+1)+4 d) y=-2f(-x+5)+1 thanks for the help !!!
  4. math

    a function f(x)has doamin {xeR/x>-4} and range {yeR/y<-1) . Determine the domain and range for each function. a) y=2f(x) b) y=f(-x) c) y=3f(x+1)+4 d) y=-2f(-x+5)+1 thanks for the help !!!
  5. Math

    Verify these answers :] Would be thankies~ 1. Determine the intervals in which the reciprocal function of f(x)= x^2+1 is increasing. a) (0,∞) b) (-∞, 0) c) (-∞,∞) d) (1,∞) Answer: D -------------------------------------- …
  6. Precalculus

    Would someone kindly verify these answers~ Thank you! --------------------------------------- 1.where does the reciprocal function of f(x)=3-x increase?
  7. Grade 11 Math functions

    y=x^2-5x+6 Domain= {xeR or 2<x<3 } Range={ } What is the range?
  8. Math

    Find values of x for which the piecewise function g(x): 1) (x+1)^2, x=<0 2) 2x+1, 0<x<33) (4-x)^2, x>=3is differentiable. I got xer, x cannot equal 3 and 0, but the answer key only has 3. WHy isn't 0 one either since the …
  9. Math

    what is the domain of (f/g)(x)? {x|x>_0} {x|x>2} {x|x>-2} {x|xer}<-- f(x)=|x|-1,g(x)=1/x What is the domain of (fog)(x) {x|x=/-1} {x|x=/0} <--- {x|xer} {x|x=/-1,x=/1} This is too hard I can't get it.
  10. Advanced Functions

    assume the function f(x) and its inverse f-1(x) are both defined for xer. give a geometric interpretation of the composite function y=f(f-1(x))

More Similar Questions