solve please an example will be in the second photo Solution:f(x) =(x+3)√4-xx²(x - 5)-34 x ≥ 042x2²xx-50x 50(x+3)√4 x = 0(-4) 3 (-1)00x+3 = 00T√4-x = 04-x = 04 = xx = 40-3This is the function we weregiven. Notice that it is alreadyin factored form.Combining this information, we4 can plot the domain of f(x) onthe number line.4We began by determining wheref(x) is defined and where it isundefined. Since f(x) has a fac-tor that is an even root, we knowthat we can only have numbersbigger than or equal to zero un-der the even root. Furthermore,since f(x) is a fraction, we knowthat we can only have non-zeronumbers in the bottom of thefraction.2Next we determine all placeswithin the domain of f(x) thatf(x)= 0. This happens when-ever the top of the fraction isequal to zero, and to solve that.equation, we set each individualfactor equal to zero and solvethose equations. Note that eachof the solutions is in the domainof f(x), so f(x) has zeros atx=-3 and 4.The zero z 4 is already plot-ted on the number line since it4 is the edge of the domain, so weadd the other zero z=-3 to thenumber line.Next we choose a test value ineach interval to help us deter-mine the sign of each interval.We indicate these test values inparentheses since they are notuniquely chosen. Show What You Know: Solving Inequalities withVarious Function TypesMAT 190 PrecalculusObjectives: The purpose of this assignment is for you to:1. demonstrate your ability to solve inequalities with various function types;2. improve your mathematical writing to include full solutions with justifications;3. integrate mathematical statements into grammatically correct expositions.Assignment: Find all intervals on which the function is positive and all intervals onwhich the function is negative:f(x) =x 3ez (x - 5)2 √2x+1°Include a detailed explanation for each mathematical step written in grammatically correctcomplete sentences within a 2-column format.

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The function is

Assignment: Find all intervals on which the function is positive and all intervals on which the function is negative: f(x) = x-3 ez (x - 5)2√2x+1° Include a detailed explanation for each mathematical step written in grammatically correct complete sentences within a 2-column format.