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Piecewise Defined Functions Evaluate the
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College Algebra
- Combining Function find f+g,fg,fg, and f/g And their domains.arrow_forwardDecomposing Functions Let f(x)=x2 and g(x)=x+1. Express (x+1)2+1 in terms of compositions of f and g.arrow_forwardMinimizing a Distance When we seek a minimum or maximum value of a function, it is sometimes easier to work with a simpler function instead. Suppose g(x)=f(x) where f(x)0 for all x. Explain why the local minima and maxima of f and g occur at the same values of x. Let gx be the distance between the point 3,0 and the point (x,x2) on the graph of the parabola y=x2. Express g as a function of x. Find the minimum value of the function g that you found in part b. Use the principle described in part a to simplify your work.arrow_forward
- Local Maximum and Minimum ValuesThe graph of a function f is given. Use the graph to estimate the following. (a) All the local maximum and minimum values of the function and the value of x at which each occurs. (b) The intervals on which the function is increasing and on which the function is decreasing.arrow_forwardMaximum and Minimum Find the maximum and minimum values of f(x)=x39x2+6 on the horizontal span of 0 to 10.arrow_forward
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